The present applicant has proposed a method of lining branches of underground pipes with a rigid plastics tube by inserting the tube into the branch through an opening thereof which is exposed from the ground and thereafter inflating the tube from inside with application of heat and pressure (see, for example, Unexamined Japanese Patent Publication HEI 1-171926). With this lining method, an excessive end portion of the tube projects from the branch into the pipe, so that the projecting end portion needs to be cut off and removed from inside the pipe after lining.
FIG. 11 schematically shows the construction of an apparatus already known for cutting off such projections inside pipes. This known cutting apparatus is adapted to cut off a projection b inside a pipe a with a saw-toothed blade 2' at the front end of a rotary drum 1' by pressing the blade against the projection in the direction of arrow. Accordingly, if the outside diameter of the drum 1' is closer to the inside diameter of the pipe a, the projection b can be cut off at a portion thereof closer to the inner surface of the pipe a. However, the pipe a generally has protrusions (now shown) such as protruding ends of other pipes attached thereto or stepped portions of joints. The drum must therefore be reduced in outside diameter so as to be movable through the pipe without striking against the protrusions. The projection then inevitably remains partly projecting inside the pipe.